= Genetic map
A genetic map turns observations of inherited <haplotypes> into an ordered account of <genetic loci> along a <chromosome>. Its distances describe <genetic recombination>, which makes the map useful for locating a <genetic locus> relative to known <genetic markers>. A <genetic map> measures inheritance separation; separation measured in <base pairs> describes positions along <DNA>. <Recombination hotspots> help explain why equal numbers of <base pairs> need not give equal <genetic map> distances. See https://www.ncbi.nlm.nih.gov/books/NBK21116/[T. A. Brown, Genomes, 2nd edition (2002), chapter 5: Mapping Genomes].
Write $d$ for the <expected value> of the number of <chromosomal crossovers> encountered along one transmitted <chromatid> between the chosen <genetic loci>, measured in <morgans>; $100d$ is the distance in <centimorgans>. This counts exchanges along that transmitted <chromatid>, rather than all exchanges in the four-<chromatid> meiotic bundle. For a short interval with very few multiple exchanges, the <recombination fraction> satisfies $r\approx d$: about $1\%$ recombinant <gametes> then corresponds to about one <centimorgan>.
For a longer interval, hidden even numbers of <chromosomal crossovers> make that approximation inaccurate. Under the <Haldane mapping function>, $d=0.2$ <morgans> gives $r\approx0.164840$; conversely $r=0.2$ gives $d\approx0.255413$ <morgans>, or $25.5413$ <centimorgans>. Applying the inverse formula to an already specified <genetic map> distance would confuse a count with a <probability>.
<Genetic map> distances add along ordered adjacent intervals because the total exchange count is the sum of its interval counts. For <independent random variables> describing counts in disjoint intervals of the <Haldane mapping function> model, the endpoint <recombination fraction> instead obeys
$$
r_{12}=r_1(1-r_2)+(1-r_1)r_2=r_1+r_2-2r_1r_2.
$$
Exactly one interval must change parental origin. Thus $r_1=r_2=0.2$ gives $r_{12}=0.32$, although the two <genetic map> distances add to approximately $0.510826$ <morgans>. The simple composition formula requires the stated <independence>; <crossover interference> can invalidate it.
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